Unique Variable Analysis: A Network Psychometrics Method to Detect Local Dependence

The local independence assumption states that variables are unrelated after conditioning on a latent variable. Common problems that arise from violations of this assumption include model misspecification, biased model parameters, and inaccurate estimates of internal structure. These problems are not limited to latent variable models but also apply to network psychometrics. This paper proposes a novel network psychometric approach to detect locally dependent pairs of variables using network modeling and a graph theory measure called weighted topological overlap (wTO). Using simulation, this approach is compared to contemporary local dependence detection methods such as exploratory structural equation modeling with standardized expected parameter change and a recently developed approach using partial correlations and a resampling procedure. Different approaches to determine local dependence using statistical significance and cutoff values are also compared. Continuous, polytomous (5-point Likert scale), and dichotomous (binary) data were generated with skew across a variety of conditions. Our results indicate that cutoff values work better than significance approaches. Overall, the network psychometrics approaches using wTO with graphical least absolute shrinkage and selector operator with extended Bayesian information criterion and wTO with Bayesian Gaussian graphical model were the best performing local dependence detection methods overall.

局部独立性假设（local independence assumption）指出，在对潜变量（latent variable）进行条件化操作后，各变量之间不再具有相关性。违反该假设所引发的常见问题包括模型设定偏误、有偏的模型参数估计以及内部结构推断失准。此类问题不仅局限于潜变量模型，同样适用于网络心理测量学（network psychometrics）领域。本文提出了一种新颖的网络心理测量学方法，通过网络建模与一种名为加权拓扑重叠（weighted topological overlap，wTO）的图论指标，来检测变量间的局部依赖变量对。借助模拟实验，本研究将该方法与当代主流的局部依赖检测方法进行了对比，这些方法包括采用标准化期望参数变化的探索性结构方程模型，以及近期提出的一种基于偏相关系数与重采样流程的检测方法。此外，本研究还对比了基于统计显著性与截断值的两类局部依赖判定方案。研究在多种偏态分布条件下生成了连续型、多分类型（5点李克特量表）与二分型（二进制）三类数据。结果表明，截断值判定方法的整体表现优于基于统计显著性的方法。总体而言，采用加权拓扑重叠结合带有扩展贝叶斯信息准则（extended Bayesian information criterion）的图最小绝对收缩与选择算子（graphical least absolute shrinkage and selector operator）的网络心理测量学方法，以及基于贝叶斯高斯图模型（Bayesian Gaussian graphical model）的加权拓扑重叠方法，是整体表现最优的局部依赖检测方法。